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In packet broadcast networks, users are interconnected via a broadcast channel. The key problem is multiple access of the shared broadcast channel. The performance of the R-ALOHA protocol for multiple access is studied in this paper. Two user models with Poisson message arrivals are analyzed; each message consists of a group of packets with a general probability distribution for group size. In the first model, each user handles one message at a time. In the second model, each user has infinite buffering capacity for queueing. Analytic models are developed for characterizing message delay and channel utilization. Bounds on channel throughput are established for two slightly different protocols. Numerical results from both analysis and simulation are presented to illustrate the accuracy of the analytic models as well as performance characteristics of the R-ALOHA protocol.